# Full text of "Analytical Mechanics"

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```MOTION OF A PARTICLE                       1
where m is a constant. But since the readings 01 the balan give the values of the kinetic reaction, equation (I) states th the kinetic reaction of the block is proportional to the accel< ation. The constant of proportionality, m, is called the me of the block. We have, therefore, the following definite for mass.
The mass of a body is a constant scalar magnitude whi equals the quotient of the magnitude of the kinetic reaction the body by the magnitude of its acceleration.
95. Measure of Kinetic Reaction. — Suppose we have se eral sets of apparatus consisting of a spring balance, a lo] elastic string, and a block, set up on a smooth horizonl table. Let two persons attend to each set of apparatus: o: to observe the readings of the balance and the other observe the acceleration of the block. Suppose the bloc to be set in motion as in the last experiment, and the pi registered by each balance observed at an instant when tJ corresponding block attains a certain definite acceleration Then if FI, F\$, F3, etc., denote the readings of the balanc and mi, m2, m3, etc., the masses of the blocks, it will be foui that the following relations hold good:
Fl_    _^l_=^J_:_:..._=X                                            /T
mx    m2    m3
Equations (II) state that when bodies have equal acceler tions their kinetic reactions are proportional to their masse Therefore equations (I) and (II) state that the kinetic r action of a body is proportional to the product of its mass I its acceleration; that is,
kinetic reaction = kmf,                      (II
where k is the constant of proportionality. When tl quantities involved in the last equation are measured in t] same system of units the constant k becomes unity, in whi< case we have
kinetic reaction = mf. '                     (III```